Question

Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance travelled by him is:

Accepted Answer

C. Let the original distance from home to hostel be $d$ miles. Onward journey time = $\frac{d}{60}$ hours. Return journey: - First half distance = $\frac{d}{2}$ miles at 25 mph $\implies$ Time = $\frac{d/2}{25} = \frac{d}{50}$ hours. - Second part distance = $\frac{d}{2} + 5$ miles at 50 mph $\implies$ Time = $\frac{d/2 + 5}{50} = \frac{d}{100} + \frac{1}{10}$ hours. Total return journey time = $\frac{d}{50} + \frac{d}{100} + \frac{1}{10} = \frac{3d}{100} + \frac{1}{10}$ hours. Given return journey time is 30 minutes (0.5 hours) more than onward journey time: $$\left(\frac{3d}{100} + \frac{1}{10}ight) - \frac{d}{60} = \frac{1}{2}$$ $$\frac{3d}{100} - \frac{d}{60} = \frac{1}{2} - \frac{1}{10} = \frac{2}{5}$$ $$\frac{9d - 5d}{300} = \frac{2}{5} \implies \frac{4d}{300} = \frac{2}{5} \implies d = 30	ext{ miles}$$ Total distance travelled = Onward distance + Return distance = $d + (d + 5) = 3

Arun's Round Trip with Bypass Road

Explanation

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